The expected values, variances and standard Deviatiations for two random variables X and Y are given in the following table
Variable | expected value | variance | standard deviation |
X | 20 | 9 | 3 |
Y | 35 | 25 | 5 |
Find the expected value and standard deviation of the following
combinations of the variable X and Y. Round to nearest whole
number.
E(X+10) = ,
StDev(X+10) =
E(2X) = ,
StDev(2X) =
E(3X-2) = ,
StDev(3X-2) =
E(3X +4Y) = ,
StDev(3X+4Y) =
E(X-2Y) = ,
StDev(X-2Y) =
E(X + 10) = E(X) + 10 = 20 + 10 = 30
SD(X + 10) = SD(X) + SD(10) = 3 + 0 = 3
E(2X) = 2 * E(X) = 2 * 20 = 40
SD(2X) = 2 * SD(X) = 2 * 3 = 6
E(3X - 2) = 3 * E(X) - 2 = 3 * 20 - 2 = 58
SD(3X - 2) = 3 * SD(X) - 0 = 3 * 3 = 9
E(3X + 4Y) = 3 * E(X) + 4 * E(Y) = 3 * 20 + 4 * 35 = 200
SD(3X + 4Y) = sqrt(Var(3X + 4Y)) = sqrt(32 * Var(X) + 42 * Var(Y)) = sqrt(9 * 9 + 16 * 25) = 22
E(X - 2Y) = E(X) - 2 * E(Y) = 20 - 2 * 35 = -50
SD(X - 2Y) = sqrt(Var(X - 2Y)) = sqrt(Var(X) + (-2)2 * Var(Y)) = sqrt(9 + 4 * 25) = 10
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